Discussion
In a 4-stroke single cylinder diesel engine, the inlet valve opens at 10° before TDC and closes at 40° after BDC. The exhaust valve opens at 25° before BDC and closes at 15° after TDC. The percentage of time for which both the valves remain closed in one cycle of the engine is
Answer: B
Both valves are closed for 40.97% of the cycle.
A four-stroke cycle takes 720 degrees of crank rotation. Find how long at least one valve is open:
\[ \begin{aligned} \text{inlet open} &= 10 + 180 + 40 = 230^{\circ} \\ \text{exhaust open} &= 25 + 180 + 15 = 220^{\circ} \\ \text{overlap at TDC} &= 10 + 15 = 25^{\circ} \end{aligned} \]
\[ \begin{aligned} \text{any valve open} &= 230 + 220 - 25 = 425^{\circ} \\ \text{both closed} &= 720 - 425 = 295^{\circ} \\ \frac{295}{720} &= 40.97\% \end{aligned} \]
Forgetting to subtract the 25-degree overlap gives 270 degrees, or 37.5%, which is not offered. The overlap counts once only, because during it both valves are open together.
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